Aerozol'nyi sloi v stratosfere

Smirnov, Boris M.

doi:10.3367/ufnr.0138.198212k.0688

Cited by 7 publications

(10 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally we note that the presented version of differential renormalization is naturally supplied with strictly four-dimensional methods of calculation of Feynman integrals, in particular integration by parts [17] which is a four-dimensional analogue of the method of integration by parts within dimensional regularization [18] and is itself based on the differential renormalization and its infrared analogue.…”

Section: Resultsmentioning

confidence: 99%

Gauge-Invariant Differential Renormalization: The Abelian Case

Smirnov

1997

Int. J. Mod. Phys. A

View full text Add to dashboard Cite

A new version of differential renormalization is presented. It is based on pulling out certain differential operators and introducing a logarithmic dependence into diagrams. It can be defined either in coordinate or momentum space, the latter being more flexible for treating tadpoles and diagrams where insertion of counterterms generates tadpoles. Within this version, gauge invariance is automatically preserved to all orders in the Abelian case. Since differential renormalization is a strictly four-dimensional renormalization scheme it looks preferable for application in each situation when dimensional renormalization meets difficulties, especially, in theories with chiral and super symmetries. The calculation of the ABJ triangle anomaly is given as an example to demonstrate simplicity of calculations within the presented version of differential renormalization. 4241 Int. J. Mod. Phys. A 1997.12:4241-4256. Downloaded from www.worldscientific.com by FLINDERS UNIVERSITY LIBRARY on 02/07/15. For personal use only.

show abstract

Section: Resultsmentioning

confidence: 99%

Gauge-Invariant Differential Renormalization: The Abelian Case

Smirnov

1997

Int. J. Mod. Phys. A

View full text Add to dashboard Cite

show abstract

“…After substitution of the functions G and F in eqs. (5,6) one finds that they remarkably satisfy the bilinear equations provided that Λ = 2. Thus, we were able to show that the single soliton solution can be built within Hirota method.…”

Section: Single Oblique Soliton Solutionmentioning

confidence: 92%

“…One can define a Mach velocity (M ) as the velocity of the obstacle relative to the sound velocity in the medium. Two-dimensional studies showed that when M > 0.37 the system loses superfluidity and start to emit pair of vortices [2][3][4][5]. Increasing the velocity showed that vortices merge in a "vortex street" [6], which were later understood as oblique solitons [7] and its exact single soliton solution determined [1,8].…”

mentioning

confidence: 99%

Hirota method for oblique solitons in two-dimensional supersonic nonlinear Schrödinger flow

Khamis¹,

Gammal²

2012

Physics Letters A

View full text Add to dashboard Cite

In a previous work[1] exact stable oblique soliton solutions were revealed in two dimensional nonlinear Schrödinger flow. In this work we show that single soliton solution can be expressed within the Hirota bilinear formalism. An attempt to build two-soliton solutions shows that the system is "close" to integrability provided that the angle between the solitons is small and/or we are in the hypersonic limit. PACS numbers: 47.40.Nm, 03.75.Kk, 05.45.Yv IntroductionThe nonlinear Schrödinger (NLS) flow is ubiquitous in many physical systems such as photorefractive crystals, and the superfluids Bose-Einstein condensates and exciton-polaritons. A fundamental problem is how a superfluid reacts to the presence of an obstacle. One can define a Mach velocity (M ) as the velocity of the obstacle relative to the sound velocity in the medium. Two-dimensional studies showed that when M > 0.37 the system loses superfluidity and start to emit pair of vortices [2][3][4][5]. Increasing the velocity showed that vortices merge in a "vortex street" [6], which were later understood as oblique solitons [7] and its exact single soliton solution determined [1,8]. Oblique solitons were long know to be unstable but it was showed that under the flow they are only convectively unstable provided that M > 1.44 [9,10]. Studies with extended obstacles also presented oblique solitons in the wake, and an analytical approach based on Whitham modulation theory was successfully applied [11]. Oblique solitons were realized experimentally in the system of exciton-polaritons [12], though for lower Mach number than originally predicted by theory. Corrections to the model including losses were able to match experimental observations [13]. Dynamics of formation and decay of oblique solitons were recently observed in [14].A key question about solitons is how they behave in collisions. As long as we know, there is no general proof about the non-integrability of the 2D-NLS. Numerical studies with two obstacles were able to generate collisions between these oblique solitons [15]. These collisions were shown to be practically elastic suggesting integrability or "close" to integrability in such system. In the same work, an analytical treatment was considered using hydrodynamical approach and the system was show to follow a 1D-NLS equation in the hypersonic limit, and collisions could be described by the well known phase shifts [16]. Numerical calculations were in good agreement with predicted phase shifts, considering that they were perturbed by previous interactions with linear waves. Since the exact single soliton (1SS) was already obtained, one might ask if an exact two-soliton solution (2SS) could be found. A possible framework to find multiple soliton solutions is the Hirota method [17,18]. In the following we build up a bilinear Hirota form of the 2D-NLS in the stationary frame relative to the obstacle. Then, we show that the single oblique soliton solution indeed satisfy this form. In the sequence we propose an ansatz to the exact solution of the two-...

show abstract

“…During the further evolution, the processes of charge separation and water phase transitions, characteristic of a cloud, can start in the aeroelectric structure. Under more special conditions (e.g., in dust storms), charge-density and electric-field perturbations on the Earth's surface can become much stronger by virtue of the intensive processes of charge separation due to friction [22].…”

Section: Diagnostic Of the Electric Environmentmentioning

confidence: 99%

Modeling of the Electric-Field Dynamics in the Atmosphere Using the Test-Structure Method

Shatalina

Mareev

Anisimov³

et al. 2005

Radiophys Quantum Electron

View full text Add to dashboard Cite

We propose the test-structure method for modeling of electric-field pulsations in the atmosphere. Numerical calculations necessary for interpretation of the behavior of experimental spectra and structure functions of the electric field are performed. Analysis of experimental data shows that the aeroelectric-field strength, being a nonlocal quantity, is formed by an inhomogeneous distribution of space charges surrounding the observation point. Quantitative assessments of the state of the atmospheric boundary layer, electro-gas-dynamic turbulence and convection parameters are discussed on the basis of spectral and structure functions of the electric field.

show abstract

Aerozol'nyi sloi v stratosfere

Cited by 7 publications

References 0 publications

Gauge-Invariant Differential Renormalization: The Abelian Case

Gauge-Invariant Differential Renormalization: The Abelian Case

Hirota method for oblique solitons in two-dimensional supersonic nonlinear Schrödinger flow

Modeling of the Electric-Field Dynamics in the Atmosphere Using the Test-Structure Method

Contact Info

Product

Resources

About